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The dynamics of modulated wave trains

About this Title

Arjen Doelman, Björn Sandstede, Arnd Scheel and Guido Schneider

Publication: Memoirs of the American Mathematical Society
Publication Year 2009: Volume 199, Number 934
ISBNs: 978-0-8218-4293-5 (print); 978-1-4704-0540-3 (online)
MathSciNet review: 2507940
MSC: Primary 35K57; Secondary 35A35, 35Q53

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Table of Contents


  • Chapter 1. Introduction
  • Chapter 2. The Burgers equation
  • Chapter 3. The complex cubic Ginzburg-Landau equation
  • Chapter 4. Reaction-diffusion equations: Set-up and results
  • Chapter 5. Validity of the Burgers equation in reaction-diffusion equations
  • Chapter 6. Validity of the inviscid Burgers equation in reaction-diffusion systems
  • Chapter 7. Modulations of wave trains near sideband instabilities
  • Chapter 8. Existence and stability of weak shocks
  • Chapter 9. Existence of shocks in the long-wavelength limit
  • Chapter 10. Applications